Donaldson R F Kepler's Third Law Calculator
Kepler's third law links an orbit's period, its size and the mass it orbits. Give any two to find the third.
The formula
In the convenient astronomical units of years, astronomical units (AU) and solar masses, Kepler's third law (as generalised by Newton from Kepler's original, Sun-only version) takes the simple form T² = a³ / M, where T is the orbital period in years, a is the semi-major axis in AU, and M is the mass being orbited in solar masses (this assumes the orbiting body's own mass is much smaller than M, which is true for every planet, moon and spacecraft in the Solar System). Set M = 1 for anything orbiting the Sun.
This is the same relationship behind, for example, working out an exoplanet's orbital period from its distance from its star, or a star's mass from a planet's period and distance.
Frequently asked questions
Does this work for moons orbiting a planet?
Yes, as long as you use the mass of the planet (in solar masses) rather than the Sun, and treat the "central mass" as whatever body the orbit is actually around.
Why solar masses and AU instead of SI units?
In those units the constant of gravitation and the awkward powers of ten cancel out, leaving the clean a³ = T² × M relationship — the same physics as the full SI version, just easier to work with for anything in a star system.
Related tools: Planet Facts Table, Orbital & Escape Velocity Calculator, Astronomical Distance Converter.
Source / Last verified: Kepler's third law (Newton's generalised form) is classical, textbook celestial mechanics; no external data source is used beyond the Sun's mass (as a reference point for "1 solar mass") from NASA/GSFC, "Sun Fact Sheet" (nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html, marked "Last Updated: 9 May 2024, DRW"), read 27 September 2026. Checked against the identity that Earth's own orbit (1 AU, 1 solar mass) gives a period of exactly 1 year.